ch8_intergranular_corrosion

Surfaces, Interfaces, and their Applications II Intergranular Corrosion
Dr. Patrik Schmutz, Laboratory for Joining Technologies and Corrosion, EMPA Dübendorf, 2013 1
8 Intergranular corrosion
In the case of intergranular corrosion, the attack is accompanied by a drastic loss of strength.
This type of corrosion mostly occurs for Al alloys (usually the copper containing ones) and
high-alloyed steels due to an erroneous heat treatment (sensitization). For austenitic CrNi
steels, the critical temperature range is between 500 and 700 °C: for temperatures around
750°C a few minutes, for 500°C a few hours are enough for sensitization. In practice, slow
cooling rates or welding operations are the causes of sensitization.
8.1 Intergranular corrosion of stainless steels
The most famous and understood example of intergranular corrosion (also denominated as
IGC) phenomenon is occurring on Cr-Ni stainless steel. The main facts about IGC are:
Observation: For a given materials, grain boundaries or areas near grain boundaries are less
noble (less corrosion resistant) compared to the inner part of grains because of a differing
composition and formation of carbides, Fig. 8.1.
As a result, the corrosive attack is localized at these “less noble” areas.
Figure 8.1: For Cr-Ni stainless steel, intergranular corrosion is related to (a) chrome
carbide formation with subsequent formation of chrome depleted zones at grain boundaries
as sketched on the composition linescan (b)
The observed damages are then not only the attack and dissolution of grain boundary areas
but also result in severe falling out of entire grains inducing macroscopic damages, Fig. 8.2.
The degradation processes can be divided in two components:
- “Electrochemical” material removal evolving at relatively small rate with local
increased corrosion at grain boundaries
- Removal of undermined grains is the most dangerous aspect regarding fast damages

Figure 8.2: For Cr-Ni stainless steel, intergranular corrosion induces subsequent grain
falling out: (a) schematic view, (b) optical cross section image through
Intergranular corrosion is the result of sensitization of the material due to “inadequate” heat
treatment. In presence of small amount of carbon in the steel, chromium reacts with carbon
during heat treatment to produce small carbides:
The diffusion process is faster at grain boundary, so that the carbides are preferentially
formed in these areas. During sensitization, chromium carbides form at the grain boundaries
(energetically favourable areas). The necessary chromium diffuses from the bulk to the grain
boundaries and chromium depletion occurs, Fig. 8.2.
A certain temperature domain ranging from 450° to 850°C is especially dangerous for
sensitization. It is important to know/control the Heat treatment temperature and time.
This critical combination is however a well-known relationship (Fig. 8.3) and specific graphs
are used as right estimation of the intergranular corrosion susceptibility for every steel. When
the temperature is low (< 400°C), diffusion is too slow to form carbides and when the
temperature is high, then bulk diffusion is sufficiently high so that carbides can be formed
everywhere and not specifically at the grain boundaries. A fast cooling (quenching) allows
avoiding sensitization, so that the process is in principle under control.
Figure 8.3: Heat treatment temperature vs. time plot presenting the domain of carbide
formation (x) and the conditions where a given stainless steel is immune (o)

The consequence of the sensitization is that the chromium-depleted areas will show a more
instable passivation and will become more susceptible to localized corrosion initiation under
the same environmental conditions (pH) compared to the inner part of the grains. The lower
chromium content of the alloy results in an increase of the critical current density (icrit) for
passivation. This is stabilizing active dissolution in presence of the cathodic oxygen reduction
reaction dominating in the neutral pH domain.
The typical potentiodynamic polarization curves for Cr-Ni steels are presented in Fig. 8.4:
a) the grains will stay passive in a given electrolyte because the only possible
equilibrium is at higher potential in the passive domain
b) The passivation of the grain boundaries will be destabilized typically by a pitting
corrosion process and an stable equilibrium in the active corrosion domain will be
reached
a) b)
Figure 8.4: Critical current density evolution: (a) in the stainless steel grains, (b) at the low
chromium containing boundaries
From a more general point of view, intergranular corrosion occurs when grain boundaries and
matrix (inner part of grains) have different electrochemical behavior. It is important to clearly
distinguish between: Active-active, active-passive and passive-passive element that are
possible for intergranular corrosion, Fig. 8.5.
The type and severity of attack depends also on the potential that can establish on the surface,
meaning that for a given stainless, external galvanic coupling can heavily influence the IGC
susceptibility. For poorly passivating material, when the whole surface can be activated for
example in acidic media, then intergranular corrosion process will result in poorly defined
broad attack at the grain boundary, Fig.8.6a. As the matrix is just dissolving a little bit slower,
this type of attack is not critical. The Active-passive process (Fig. 8.6b) is much more critical
because the grain surface is protected and therefore, the grain boundaries dissolution will
undermine the grains and affect dangerously the materials integrity. With a passive film
supporting the cathodic reduction, additional corrosion acceleration through galvanic
coupling will take place. The last type of IGC is the passive –passive situation, Fig. 8.6c. If
the chromium content is varying from the grain inner to the boundary, then the stability of
passive film will be lower at the boundary. This means that very slowly, passive grain
boundary attack will take place. The dissolution rates are typically a few tens of
micrometer/year, the problem being that the formed directed attacks can be initiation sites for

crack propagation and dramatic failures in presence of stresses (Stress Corrosion Cracking,
Fatigue).
Figure 8.5: The different types of intergranular attack types depending on the passivation
ability and degree of sensitization of a stainless steel
Figure 8.6: Optical cross section images of the three different types of intergranular attacks:
(a) active - active, (b) active - passive, (c) passive – passive processes

Measures to avoid intergranular corrosion of steel
1) From a materials perspective:
- Heat treatment at higher temperature (1050-1100°C) followed by quenching
- Decrease of the carbon content of steel (not always possible because it decreases the
machinability of the steel)
- Addition of Titanium, Niobium, Tantalum (higher affinity for carbide formation than
Chromium)
Intergranular corrosion on high-alloyed steel can be avoided when steel with low carbon
content or with additional titanium in the alloy is used. Low carbon content makes carbide
formation impossible, while alloying with titanium (Ti = 5 * C concentration) leads to
formation of (non interfering) titanium carbides, and the chromium content remains
unchanged through the whole grain boundary.
2) From a design and construction perspective:
- Control of the temperature flow during welding. Heat affected zones away from the
weld areas are often the location of IGC failure, Fig.8.7. This problem is by far the
most acute as it is not easy to avoid the intermediate temperature domain during
welding. It is currently the major still remaining cause of IGC failure for steel.
Figure 8.7: Intergranular corrosion attacks taking place at heat affected zone (sensitized) of
welds.

8.2 Intergranular corrosion of Al-alloys
The second example presented in this chapter is related to the intergranular corrosion of Al-
alloys. In this case, the understanding of the processes is much lower compared to stainless
steel. One of the difficulties lies in the complexity of the microstructure of these alloys and
their local reactivity (see chapter 5). Another aspect which makes Al-alloys corrosion more
difficult to describe is the different processing route used to obtain the final secondary
products. This starts from production through casting, extruding and/or rolling and in
addition, their respective solution heat treatments (SHT) and artificial ageing. For this reason,
it is important to know the complete processing route for Al-alloys.
8.2.1 Typical alloy microstructures and nomenclature
In the examples presented below, specimens were prepared from commercial 1.9 cm thick
2024-T3 plate stock. For the plate material, samples with three different orientations (see Fig.
8.8), i.e. longitudinal (L), long transverse (LT) and short transverse (ST) sections were
prepared using a diamond saw. The grain size, elongation and grain boundary density will
vary accordingly from one orientation to the other. The T3 tempers were produced by
artificially aging 2024-T3 slices, previously cut from the plate, at 190°C in an air furnace for
2.5 h followed by air cooling, respectively. Solution heat treated 2024 samples were also
prepared from the as-received 2024-T3 plate and sheet materials. The solution heat treatment
was conducted in an air furnace at 492°C for 1 h, followed by either water quenching or
furnace cooling. The effect of artificial aging on the mechanical properties was determined
using microhardness measurements.
All samples for electrochemical experiments were ground mechanically and polished through
a series of silicon carbide (SiC) papers (up to 800 grit) in ethanol. No water was used during
polishing in order to minimize corrosion during sample preparation especially of the very
susceptible intermetallics. After polishing, the samples were degreased with ethanol before
attachment to the side of a Plexiglas cell (typical three electrode cell) by pressing against a
teflon knife-edge O-ring (hydrophobic and avoiding crevice corrosion effects) to expose an
area of about 1 cm2
for the experiments. The solution for the experiments was 1 M NaCl.
Figure 8.8: Plane definition according to rolling direction of Al –alloy sheet and plates

The 2024 plates have a typical elongated pancake-shaped grain structure. Grains were
elongated in both the longitudinal and long transverse directions. This directionality of
elongated grain structure is particularly important in regard to localized corrosion growth
kinetics.
The microstructures of 2024-T3 were characterized using optical metallography, scanning
electron microscopy (Philips XL30 FEG-SEM) and transmission electron microscopy (Philips
CM200 TEM). Foils for transmission electron microscope (TEM) examination were prepared
by electropolishing in a twin-jet electropolishing apparatus using a 30% nitric acid in
methanol at -30 to -50 °C. In naturally aged 2024-T3, it is believed that the matrix contains
homogeneous coherent precipitates, denoted as GP zones, as well as fine hardening
precipitates (S` Al2CuMg). Figure 8.9 are typical TEM micrographs from the 1.9 cm thick
plate showing the high density of plate shaped hardening precipitates (S`Al2CuMg) in 2024-
T3. In addition, scattered through the matrix are a lot of large and rod shaped particles
containing Al, Mn, and Cu (possibly Al20Mn3Cu2), Fig 8.9a. There was “little” evidence for
the existence of precipitate-free zones (PFZ) along the grain boundaries in T3 temper
although the formation of PFZ adjacent to the grain boundaries during quenching has been
reportedin literature. However, many rod shaped precipitate particles can be seen in GB
regions, Fig. 8.9b. They all had a similar shape, but were identified by EDS as having
different compositions: very close to Al2Cu (very little Mg), Al2CuMg or Al20Mn3Cu2 with
no Mg. The Mn and Curich particles are thought to pin grain boundaries, thus retarding
recrystallization, and resulting in the retention of the elongated grain structure.
Figure 8.9: Transmission electron micrographs of AA2024-T3 plate material showing (a)
plate-like S`(Al2CuMg) precipitates, (b) rod-like precipitates in matrix and grain boundaries.
Schematically, the reactivity of such grains boundaries can be seen on Fig. 8.10. Very
reactive nm-scale Cu-rich intermetallic particle are aligned in the grain boundaries. Around
them, a Cu depleted zone is formed with low electrochemical potentials related to the almost
pure Al nature of this zone. The grains have an intermediate potential and show better
passivation and localized corrosion resistance compared to the depleted zone due to the
presence of alloying elements in solid solutions. The exact passive layer stabilization
mechanisms in the grains are not yet very clear.

Figure 8.10: Typical composition gradients at the intergranular corrosion susceptible grain
boundarie in copper containing alloys.
8.2.2 Example of intergranular corrosion attacks
The difficulty of predicting which type of localized corrosion process is relevant for a given
alloys – processing – ageing combination is shown on the following metallographic cross –
section. They have been performed after the bottom surface was exposed to aerated NaCl
solution. The sample shown on the left image had a too low ageing temperature with an
extremely high susceptibility to intergranular corrosion. Increasing by 20°C the ageing
temperature, the localized corrosion process is totally different with only pitting detected. It
has to be noted that these 20°C are almost in the error range considering industrial
production.
Figure 8.11: Similar 2024T3 alloys artificially aged at two relatively close temperature:
(left) 16h at 170°C resulting in IGC attack and (b) 20h at 190°C where only large pits at
found
In order to describe this switching from IGC to pitting corrosion mechanisms, anodic
potentiodynamic polarization experiments were performed in deaerated 1.0 M NaCl to

determine the breakdown potentials of 2024 as a function of sample orientation relative to the
rolling direction. The solution was Ar-deaerated before the polarization experiment because
otherwise, the Al alloy surface would experience spontaneously localized corrosion upon
immersion. The solution was continuously purged with Ar during the measurement. Each
sample was exposed to the solution for 35 min prior to the start of the measurement, and then
potentiodynamically polarized from -30 mV below the open circuit potential to a potential
above the breakdown potentials at a scan rate of 0.1 mVs-1
. No IR compensation or correction
was made during polarization measurements. The breakdown potentials were taken as the
points in the anodic polarization curve at which the current increased sharply, Fig.8.12.
Potentiodynamic polarization experiments were performed on ST, L, and LT samples in
deaerated 1 M NaCl to test the influence of sample orientation. Figure 8.12 shows that the
current increases sharply above the first breakdown potential E1. However, instead of
increasing monotonically with increasing potential, the current reaches a maximum at a
potential labeled Ec and then decreases by as much as a factor of 10. Above a second
breakdown potential, E2, the current increases again. The two breakdown potentials are
almost independent of the sample orientation and potential scan rate. The more active one,
E1, occurs at about -670 to -700 mV SCE, and the nobler one, E2, occurs at about -590 to
-610 mV SCE. Ec was in the range of -630 to - 650 mV SCE. This current maximum is a
reproducible feature of the potentiodynamic polarization curves for the three alloy directions
of 2024-T3. It should be pointed out that a two-breakdown potential polarization curve is a
summation of current from two different localized dissolution processes. Even though it
seems that the second breakdown potential results primarily from IGC growth, IGC can
initiate below the second breakdown potential. At lower potentials, the current associated
with IGC is masked by the larger current associated with the transient S phase dissolution
inducing pitting. So it should not be assumed that IGC is not possible below the second
breakdown potential determined potentiodynamically.
Figure 8.12: Potentiodynamic anodic polarization curves for the different orientations of the
2024-T3 plate in Ar-deaerated 1 M NaCl

The presence of two breakdown potentials so close together in the anodic polarization curves
is an important feature of localized corrosion of 2024-T3 in chloride solution. This indicates
that there are two phases in the 2024-T3 microstructure, with different dissolution potentials,
responsible for two different forms of localized corrosion. The next characterization step is
now to find out the reason for the current peak, i.e. the decrease in current with increasing
potential above Ec. In order to determine the causes responsible for each of the breakdown
potentials in the polarization curves of 2024-T3, longer potentiostatic polarization
experiments were performed. The following sequence of electrochemical experiments has
been chosen:
(i) first cyclic anodic polarization experiments
(ii) followed by partial reverse scan down to a selected potential
(iii) potentiostatic polarization at this potential, to examine the corrosion propagation and
possibly the repassivation of localized corrosion during the reverse scan.
The samples were first potentiodynamically polarized from the open circuit potential to
-520 mV SCE, which is well above E2, and then scanned in the reverse direction to -620,
-660, or -800 mV, Fig.8.13d. The samples were held at the final potentials for 20 hours, and
then metallographically cross sectioned to determine the corrosion morphology. Figure 8.13a
to c shows some typical metallographic cross sections of those samples. It is clear that IG
attack depth decreased with decreasing potential on the reverse scan, which suggests that IGC
growth was not sustained when the potential was decreased to a certain value (Er
repassivation potential for IGC). The attack morphology is more like pitting at -660 mV (Fig.
8.13b) which lies at the boundary of the potential transition domain and definitely only pitting
at -800 mV SCE, Fig. 8.13c. Comparison with samples held at -620 mV (Fig. 8.13a), clearly
shows that in this case localized corrosion quickly turns into intergranular corrosion
propagation. The elongated nature of the grains in this Al sheet results furthermore in a
directed attack parallel to the sheet surface.
Note: This special case of directed intergranular attack is called Exfoliation corrosion and is
typical for IGC susceptible materials sheets.
The higher potential was associated with the dissolution of the Cu depleted zone along the
GB (i.e. IGC), and the noble one corresponded with pitting of the grain bodies.

Figure 8.13: Metallographic cross sections of 2024T3 samples potentiodynamically polarized
to -620mV on reverse scan and held the potential for 20 h, (b) to -660mV and held the
potential for 20 h, (c) to -800 mV SCE and held the potential for 20 h in deaerated 1M NaCl,
(d) cyclic polarization curve showing the potentials for the potentiostatic experiments.
Measures to avoid intergranular corrosion of aluminum alloys
1) From a materials perspective:
- Choose the appropriate heat treatment to avoid formation of cathodic intermetallic
particles and pure aluminum areas along the grain boundaries
- This process is unfortunately less controllable (very much dependent on treatment
temperature) then for steel because of the complex
2) From a design and construction perspective:
- Similar to the case of steel, control of the temperature flow during soldering.

8.3 Synchrotron measurements - Tomography
8.3.1 Principle and setup
Figure 8.14: Sketch of the working principle of a synchrotron.
The principle of tomography is illustrated in Fig. 8.14. Electrons circulate with speed close to
light through the storage ring. Due to the radial acceleration applied with magnets X-rays are
emitted by the electrons. The X-rays are guided into a beam hut where they are used for
experiments. In the following, a short introduction into synchrotron principles is given.
The unique properties of synchrotron radiation are its continuous spectrum, high flux and
brightness, and high coherence, which make it an indispensable tool in the exploration of
matter. The wavelengths of the emitted photons span a range of dimensions from the atomic
level to biological cells, thereby providing incisive probes for advanced research in materials
science, physical and chemical sciences, metrology, geosciences, environmental sciences,
biosciences, medical sciences, and pharmaceutical sciences.
This breadth of problems requires an extensive suite of probes. The basic components of a
beamline, however, share general similarities as shown in the schematic diagram below
(Fig. 8.15).
Figure 8.15: Possible synchrotron measuring techniques.

The fundamental parameters that are used to perceive the physical world (energy, momentum,
position, and time) correspond to three broad categories of synchrotron experimental
measurement techniques: spectroscopy, scattering, and imaging (e.g. tomography). By
exploiting the short pulse lengths of synchrotron radiation, each technique can be performed
in a timing fashion.
Spectroscopy is used to study the energies of particles that are emitted or absorbed by
samples that are exposed to the light-source beam and is commonly used to determine the
characteristics of chemical bonding and electron motion.
Scattering makes use of the patterns of light produced when x-rays are deflected by the
closely spaced lattice of atoms in solids and is commonly used to determine the structures of
crystals and large molecules such as proteins.
Imaging techniques use the light-source beam to obtain pictures with fine spatial resolution
of the samples under study and are used in diverse research areas such as cell biology,
lithography, infrared microscopy, radiology, and x-ray tomography.
High brightness has the following advantages:
o short measuring time for a given experiment
o measurement on very small samples (e.g. crystals of 30 µm)
o microscopy and spectroscopy with excellent resolutions
o high coherence of the synchrotron light allowing images with phase contrast
o compact optical components (mirrors, monochromators), small aberration
effects
8.3.2 Microtomography
Microtomography is a special form of tomography where submicrometer spatial resolution is
achieved. The principle of tomography works as follows:
X-rays interact with matter by several processes: photoelectrical absorption, elastic
(Rayleigh) and inelastic (Compton) scattering and electron-positron pair production. In the
next examples, the focus is on X-rays in the energy range 10 - 25 keV and mainly interested
in absorption in general. The absorption of X-rays is given as described by the Beer-Lambert
Law.
N is the number of photons for a given energy. µ is the linear attenuation coefficient. The
dependency of the linear attenuation coefficient on the photon energy is given in Fig. 8.16.
Different absorption edges can be seen (e.g. at 0.7 keV) and a general decrease of absorption
with raising energies.

Figure 8.16: Adding up all the processes contribution to the attenuation of a X-ray beam
propagation through matter, i.e. the atomic photoelectric cross-section τ, the coherent
(Rayleight) scattering cross-section σcoh and the incoherent (Compton) scattering cross-
section σincoh one obtains the total linear attenuation coefficient.
To measure the linear attenuation coefficient, the X-ray beam behind the specimen is
detected. An incident beam (N0 photons or intensity I0) crossing a specimen is absorbed /
scattered by the material. This lower intensity (N or I) of the X-ray beam is detected. On the
basis of this absorption, the linear attenuation coefficient can be determined. Measuring the
linear attenuation coefficient the material, the path length through the material (x) or the
energy (E) can be determined. In the experiments presented later, the energy and the thickness
of the material is known and therefore the material can be determined. In tomography the
linear attenuation coefficient is measured in three dimensions. Or in other words, the linear
attenuation coefficient can be described as function of the room coordinates. This is possible
as about 700 two dimensional images from different angles are taken and then via back
projection algorithm calculated into a three dimensional structure. In a tomogram, the linear
attenuation coefficient is displayed as grey level in a three dimensional room.
In the present experiments, used aluminums alloys are inhomogeneous in their microstructure
and therefore the X-ray beam crosses different elements, Fig. 8.17. The inhomogeneities of
the microstructure are mirrored in the difference in the linear attenuation coefficient.
Figure 8.17: the X-ray beam penetrates the orange specimen. Different phases (marked with
colours) are passed. The specimen can be rotated and therefore passes the X-ray beam in
different sections of the material. As a result the attenuation coefficient can be calculated as
a function of the position within the material.

X-ray microtomography experiments were performed at the SLS X04SA Materials
Science Beamline at the Paul Scherrer Institute (PSI), Villigen. Acquisition was carried out
at a 17 keV X-ray energy with a double Si111 crystal monochromator. Fast acquisition of
the radiographs was performed at 20 keV with a double multilayer monochromator. The
detector CCD chip was read out with 1024x1024 pixels, giving a final practical resolution
of about 3 µm. 720 2D radiographs were taken for the subsequent reconstruction
procedure. The settings used for fast acquisition of the data lowered the acquisition time
from 1h to 10 minutes. To measure corroded volumes, the tomograms were converted into
binary images and a greyscale threshold was defined to allow separation of corroded and
not-attacked regions. The set-up is designed so that a pin can be fully immersed in solution
during tomographic measurements, whereby the dimensions of the pin are adjusted to
allow short acquisition times (see Fig. 8.18).
Figure 8.18: Sketch of exposure cell: a
pin of 500µm diameter was fully
immersed in the solution confined in
silicone rubber tubing. The field of view
marks the area where the beam
penetrated the specimen.
Samples for X-ray tomography experiments were first machined to 3 mm diameter rods,
and then the upper 2 mm was turned down to 0.5 mm diameter pins. The samples were
lacquered with Stopping Off Lacquer to cover all but the to the X-ray beam exposed part
of the pin. For samples investigated in-situ, a silicone rubber tube with 3 mm internal
diameter was slipped over the outside of the 3 mm rod to form a cell around the pin, and
the cell was subsequently filled with solution.
In combination with X-ray synchrotron microtomography characterization, local,
microelectrochemically-controlled measurements were also performed. The
microelectrochemical technique used was a modified microcell technique developed at
Empa Dubendorf, Fig. 8.19. This setup with controlled exposed areas on top of the pin,
allows initiating and controlling a single localized corrosion attack. The reconstructed
tomograms with its attacked volume can then be correlated with the total current passed in
the electrochemical cell and correlated corrosion propagation rates with microstructural
features for example.

Figure 8.19: (a) Schematic sketch of the electrochemical tomography setup. The microcell
is mounted on top of the specimen, which is in the beam (CE = counter electrode, WE =
working electrode, RE = reference electrode); (b) radiograph of the capillary positioned
on top of the pin.
8.3.3 Examples of intergranular attacks monitored by Synchrotron Tomography
For the tomography experiments, the corrosion processes of the 6016 and 6111 alloys have
been considered this time (these alloys are less corrosion susceptible compared to the
2024-T3 alloy presented before) and 3 types of corrosion experiments were performed:
1) in-situ during immersion of samples in 0.7M HCl;
2) in-situ in 2.5M HCl
3) ex-situ after 0.7M, 2.5 M and 5 M HCl solution exposure.
Table 8.1: Composition of 6016 and 6111 measured by optical emission spectroscopy.
wt% Mg Si Fe Mn Cu Cr
AA6016 0.35 1.05 0.19 0.08 0.07 0.01
AA6111 0.61 0.80 0.26 0.21 0.70 0.02
In Figure 8.20, an ex-situ SEM image of a corroded AA6016 pin used in the tomography
experiments is shown, providing an overview of the corrosion damage observed upon
immersion in aggressive HCl electrolyte. The pin was immersed for 45h in 0.7M HCl.
External investigations, even if they show visible signs of attack, would tend to indicate
that this alloys resisted pretty well to localized and intergranular corrosion.

Figure 8.20: SEM image of a pin with
heavy traces of corrosion. AA6016
immersed for 45h in 0.7M HCl.
The previously-mentioned heterogeneous grain structure of Al-alloys can be seen, as the
pin is not attacked homogeneously. However, the extent and morphology of the corrosion
attack inside the pin is not predictable from such surface observation.
Note: The immersion times for the next examples are up to 7h and monitored in-situ with
1 scan (X-ray tomography measurement) per hour for 0.7M HCl. In-situ experiments with
specimens immersed in 2.5M HCl were monitored with 1 scan every 15 minutes.
The 6061 alloy was immersed in a more aggressive 2.5M HCl solution and the propagation
of intergranular corrosion was monitored by X-Ray tomography. Figure 8.21a displays the
reconstructed pin in grey, the intermetallics are white and the attacked areas filled with
lower density solution are dark. This way, it is possible to clearly distinguish that
intergranular attack propagate deep into the Al alloys. Besides the propagation rates that
can be retrieved, two very important observations can be mentioned:
(i) The surface is not very much corroded except for the grain boundaries and this
gives the previously mentioned misleading impression that this Al-alloys is
corrosion resistant also in very aggressive environments
(ii) The local aggressivity of the solution in the intergranular attack path is increasing
as a function of depth. In the middle of the pin, very strong directed attack called
“Exfoliation Like Attack” (ELA) is visible. This phenomenon would not have been
detected ex-situ because of the difficulty to located one of these path with
metallographic cross sections.

a) b)
Figure 8.21: (a) Intergranular corrosion attack of 6061 Al alloy immersed 7h in 2.5M HCl
characterized by X-Ray microtomography, (b) optical picture of the simple immersion
setup.
In the next example, the different types of localized corrosion are even more evidenced. A
more corrosion susceptible 6111 (higher Cu content) alloy has been investigated by X-Ray
microtomography in 0.7M HCl, Fig. 8.22. A newly-revealed phenomenon of slow-
dissolving surface-deformed layer and the transition from intergranular corrosion (IGC) to
exfoliation-like attack (ELA) are illustrated. Figure 8.22 shows various corrosion
phenomena observed inside a corroded pin. The black regions in the grey aluminum matrix
are corroded areas, whereas the small white spots represent intermetallic particles. Figure
8.22a shows a 3D reconstruction including LT and L planes. Two types of attack can be
observed; one is a typical intergranular corrosion (IGC), while the other as mentioned
previously is referred to as “exfoliation-like attack” (ELA). The term “exfoliation-like”
corrosion is used to indicate morphologies similar to exfoliation corrosion. In contrast to
conventional exfoliation corrosion, ELA is not present along the surface (see Fig. 8.13a)
and the mechanism might be different.
IGC, seen as thin black paths within the Al matrix, follows the grain boundaries without
indication of a specific preferred direction as would be expected for elongated grain. Here
the grain boundaries are selectively attacked and single grains may be completely
surrounded by IGC, but single corrosion paths of several hundred µm in length along grain
boundaries can also be observed. ELA-type corrosion can start in the bulk of the material.
Figure 8.22b illustrates this and the high aspect ratio (length to width) of the ELA. It is
also clear that ELA is strongly directed and follows the L direction in planes parallel to the
former sheet surfaces (orthogonal to ST direction). A preferred location for ELA at the pin
surface or pin center was not found. A further observation is that ELA is not hindered by
grain boundaries and can be in the range of mm length. Grain can furthermore completely
dissolve in the inner part of the materials, but the fact is that even if the inner of the pin is

completely dissolved (Fig 8.22c), this heavy corrosion attack is still not visible from
outside. Responsible for this, is the so called deformed surface layer.
Figure 8.22: Reconstructed X-ray tomograms. Various ex-situ views of corrosion
sites within an AA6111 pin exposed to 0.7 M HCl solution for 7h: a) 3D view and
section; b) L plane (top view) taken out of the lower region of the pin; c) ST plane
(parallel to sheet surface) showing the whole pin. Clearly visible is the exfoliation-
like attack, the intergranular corrosion and the special behavior of the surface-
deformed layer.
Figure 8.23 shows a cut through a rolled Al sheet and deformed surface layers are generic
features of such aluminium sheet products.
The characteristics of deformed surface layers:
Nano-crystalline (grains < 50 nm)
Second-phase inclusions (oxides, lubricant)
Intermetallic particle distribution different from bulk.
In principle these layers are more susceptible to corrosion initiation because of large amount
of defects present but it this case they can visibly show other advantages concerning slower
active dissolution. It is not yet clear if the grain size can play such a big role on the corrosion
mechanisms.

Figure 8.23: TEM image of an ultramicrotomed Aluminium alloys, showing the 450nm fine
grained surface deformed layer with different corrosion susceptibility in very acidic media
8.4 Mathematical modelling concepts of localized corrosion
As already discussed starting at chapter 6, localized corrosion occurs on passivated metal
surfaces which are protected by a thin poreless oxide layer. Under the influence of aggressive
anions, such as chloride, a strong localized attack takes place causing the formation of pits
ranging in size from nano- to millimetres. It is generally agreed that stable localized corrosion
is preceded by the development of aggressive chemical and electrochemical conditions in the
pit which lead to the local activation of the metal. The pit solution is usually defined in terms
of its pH and chloride concentration.
During pitting, metallic ions are present in the solution as a consequence of metal dissolution.
These species also undergo homogeneous reactions forming more complex species. The
species are transported to and from the pit by diffusion, migration, and convection. By
analysing the local chemistry of corrosion pits in aluminium alloys exposed to sodium
chloride solution, the relevant species, heterogeneous reactions on the metal surface, and
homogeneous reactions in the solution can be identified. Because direct measurement of local
electrochemical and chemical behaviour during pitting can be difficult, mathematical models
can help to understand the mechanisms of localized corrosion phenomena.
The purpose of the presented investigation is to simulate the local chemical environment of
corrosion pits in aluminium alloys for a microcapillary geometry using mathematical
modelling. In this experimental setup, a fine microcapillary filled with electrolyte is placed on
the specimen which is mounted on a microscope stage allowing for the precise positioning of
the capillary (Fig. 8.24a). The end diameter of the capillary can be varied from about 10 µm
to 1 mm, depending on the experimental requirements (Fig. 8.24b). The reference and the
counter electrodes are connected to the capillary to allow electrochemical control of the
surface under investigation.

Figure 8.24: (a) Assembled microcell; (b) Capillaries used for microelectrochemical
measurements.
A special attention is paid to the modelling of a real experimental capillary setup which,
mathematically speaking, appears as different boundary conditions applied at the capillary
wall. Moreover, the modelling results, in turn, can lead to improving the electrochemical
experimental setup and definition of new experimental developments to measure critical
chemical parameters defined by the modelling.
8.4.1 Mathematical equations
In this first simplified model, a dilute solution has been assumed, thus, the physical
parameters are independent of the species concentrations. The material balance for each
chemical species, i, is given by
=
∂
∂
t
ci
iN⋅⋅⋅⋅∇∇∇∇−−−− iR+ (Eq. 1)
where the flux density of each dissolved species is
iiiiii cDFcuz ∇∇∇∇−−−−∇∇∇∇−−−−==== ΦN vic+ . (Eq. 2)
Here, zi, ci, and Di are the charge number, concentration, and diffusion coefficient of species i,
respectively. The convection term in the model is zero (i.e., the bulk velocity, v, is 0). The
electrostatic potential in the solution is Φ and F is the Faraday constant. The mobility, ui, is
estimated by the Nernst-Einstein equation, ii RTuD = , where R is the universal gas constant
and T the absolute temperature. The production rate per unit volume, Ri, involves
homogeneous chemical reactions in the bulk solution.
Because the potential, Φ, is also an unknown variable, one more equation is required, in
addition to the equations (Eq.1) written for each individual species. To a very good
approximation, the solution is electrically neutral,
∑ =
i
ii cz 0 . (Eq. 3)
(a)
(b)
2 mm

In this model, the equilibrium state in the solution is not assumed and all terms, Ri, in the
homogeneous reactions are treated explicitly using kinetic constants found in the literature
(see lecture slides for more details)
8.4.2 Local chemistry of corrosion pits in aluminium 2024 alloy in sodium chloride
In this chapter, the direct active dissolution attack of the exposed metal is modelled, assuming
that pitting initiation has already occurred. Two types of reactions are considered: (1)
electrochemical reactions at the metal-solution interface (heterogeneous reactions) and (2)
reactions occurring in the solution (homogeneous reactions). The first type can be
introduced through the boundary conditions at the metal interface, whereas the second type
through the knowledge of the chemical reactions in the solution and their reaction rates.
Three metallic species, Al3+
, Cu2+
, and Mg2+
, appear at the metal surface as a result of
heterogeneous electrochemical reactions:
Al° → Al3+
+ 3e-
(1)
Cu° → Cu2+
+ 2e-
(2)
Mg° → Mg2+
+ 2e-
. (3)
Sodium chloride solution with a bulk concentration of 1 M and pH of 6 was used as an
electrolyte in this work. Therefore, the four species, characteristic for this solution, Na+
, Cl-
,
H+
, OH-
, should be present in the models together with the reaction for water dissociation (4):
H2O H+
+ OH−
(4)
The metallic species, Al3+
, Cu2+
, and Mg2+
, can undergo hydrolysis reactions and can also
react with the chloride ions. It was found experimentally that the solution in pits and crevices
in aluminium has lower pH values compared to the bulk solution, usually below 4. Therefore,
for the modelling of the solution in the pits, only species which are stable at low pH have to
be considered.
Al related species
The analysis of species stability in aqueous solutions with pH values below 4 for Al
hydrolysis products and the species obtained as a result of homogeneous reactions between
chloride and Al3+
ions and Al hydrolysis products was conducted. It was found that the
following Al related species should be included in the model: Al3+
, AlOH2+
, Al2(OH)2
4+
,
AlCl2+
, Al(OH)Cl+
, and Al(OH)2Cl. The corresponding homogeneous reactions are listed
below:
Al3+
+ H2O AlOH2+
+ H+
(5)
2Al3+
+ 2H2O Al2(OH)2
4+
+ 2H+
(6)
Al3+
+ Cl-
AlCl2+
(7)
AlOH2+
+ Cl-
Al(OH)Cl+
(8)
AlCl2+
+2H2O Al(OH)2Cl + 2H+
(9)
Al(OH)Cl+
+ H2O Al(OH)2Cl + H+
(10)

Al3+
Al bulk
z
symmetryaxis
capillarywall
Na+ Cl-
AlOH2+ AlCl2+
Al(OH)Cl-
Al(OH)2Cl
H+ OH-
Al3+
Al bulk
z
symmetryaxis
capillarywall
Na+ Cl-
Al3+
Al bulk
z
Al3+
Al bulk
Al3+
Al bulk
z
symmetryaxis
capillarywall
Na+ Cl-
AlOH2+ AlCl2+
Al(OH)Cl-
Al(OH)2Cl
H+ OH-
The following boundary conditions were applied:
• On the capillary top: 0, =Φ= ∞
ii cc , where cNa
∞
and
cCl
∞
were set to the bulk solution concentration, usually
1 M for most calculations; for models with H+
ions,
cH
∞
= 1 · 10-6
M, giving a pH of 6; ci
∞
for all Al
containing species were set to zero.
• The symmetry axis is on the left side in Figure 2.
• On the right side (capillary wall) two types of
boundary conditions were imposed: either “insulating
wall” where the normal fluxes of all species were zero
( 0=⋅ iNn ) or the condition identical to that on top of
the capillary, 0, =Φ= ∞
ii cc , which we refer to as
“no walls”.
• The Al bulk boundary surface is assumed to be
insulating and the pit boundary surface to be actively
dissolving according to Al Al3+
+ 3e−
with a
constant current density, jAl . Therefore, the flux of
Al3+
at the pit surface can be written as
F
jAl
3
=⋅ +3
Al
Nn
with j taking discrete values from 1 µA/cm2
to 5
Cu related species
The Cu2+
ion at ordinary concentrations begins to hydrolyze above pH 4 and precipitates the
oxide or hydroxide soon thereafter. The principal cationic hydrolysis product is the dimmer
Cu2(OH)2
2+
, however, it is also not present at pH below 4. Cu2+
forms relatively weak halide
complexes, therefore, only Cu2+
ion should be included in models.
Mg related species
It seems likely that MgOH+
and Mg4(OH)4
4+
are the only hydrolysis products of Mg2+
formed
in the solution, however neither of these two species is stable enough to be very significant in
the aqueous chemistry of magnesium except for quite alkaline solutions. Therefore, for the
acidic environment found in pits, both these ions should not be taken into account. Therefore,
only Mg2+
ion should be included in models.
Based on the solution chemistry analysis, the following species should be included in the
model: Na+
, Cl-
, H+
, OH-
, Al3+
, AlOH2+
, Al2(OH)2
4+
, AlCl2+
, Al(OH)Cl+
, Al(OH)2Cl, Cu2+
,
Mg2+
.
8.4.3 Modelling of anodic dissolution of pure aluminium
Geometry and boundary conditions
The geometry of the model has been chosen to simulate the geometry of the electrochemical
cell for the microcell technique, Fig. 8.24. Therefore, a cylindrical geometry has been chosen
as a first approximation for the model, with a hemispherical pit of a radius of 10 µm located
in the centre of the cylindrical capillary (Fig.8.25); the coordinate z = 0 is at the pit bottom.
Such size and shape parameters are typical for the early growth stage of naturally occurring
corrosion pits. The capillary height is 10 mm and capillary end radius is varying from 100 µm
(10 times exceeding the pit radius) to a macroscopic radius of 10 mm, where the influence of
the capillary wall should be negligible.
Figure 8.25: Model
geometry and
boundary
conditions

In the first model, a change in the pit shape due to aluminium dissolution (“moving
boundary”) is neglected. It is assumed that the cathodic reactions occur very far from the pit
surface.
All calculations in this work were carried out on a Pentium processor with the COMSOL
software assuming a steady-state condition (Eq.1, 0=
∂
∂
t
ci
).
Model with 3 species Na+
, Cl-
and Al3+
and no homogeneous reactions
Consider a simple model with three ions, Na+
, Cl-
and Al3+
and with the hemispherical pit
geometry shown in Fig. 8.25 and assuming a capillary with an end radius of 10 mm. The
boundary conditions applied are: “no walls” at the capillary wall and active metal dissolution
with a constant current density, jAl, of 4 A/cm2
at the pit surface (the value was obtained from
the fit of the experimental current data). Adaptive meshes consisting of triangular Lagrange-
quadratic elements with a more dense mesh inside the pit and less dense outside were
employed. First, the influence of the mesh quality on the results was checked. Several meshes
with a sequential increase of element numbers inside and in the vicinity of the pit were
generated. Fig. 8.26 presents results obtained assuming a variable number of elements. For all
calculations done in this work, meshes with more than 5000 elements were employed.
Figure 8.26: Concentration of Na+
and the potential at the pit bottom vs. the number of
Lagrange-quadratic elements, calculated assuming a dissolution current density of 4 A/cm2
and a bulk chloride concentration of 1 M.
In order to simulate the capillary geometry, the “insulating wall” boundary condition was
imposed at the capillary wall. A number of models were generated with a hemispherical pit
having a radius of 10 µm located in the middle of the cylindrical capillary which has an end
radius, rcap, varying from 100 µm to 10 mm. Because the shape of the capillary used for the
micro-electrochemical cell (Fig. 8.24b) differs significantly from the cylindrical one, a
number of models were generated with a digitized real capillary shape and different end
capillary radii (rcap for these models). Calculations were performed assuming a dissolution
0.142
0.1425
0.143
0 5000 10000 15000 20000
number of elements
[Na
+
],[M]
0.0499
0.05
0.0501
potential[V]
[Na+]
potential
+

current density, jAl, of 1 A/cm2
and a solution of NaCl with a bulk chloride concentration of 1
M and a bulk pH of 6 as an electrolyte
It follows from Fig. 4 that for rcap/rpit < 100, the application of “insulating wall”-boundary
condition affects species concentrations: for rcap/rpit = 100 it leads to a difference of 3-4 % in
the values of potential and species concentrations, whereas, for rcap/rpit = 50, there is a
difference of 10-16 %. For rcap/rpit < 20, the capillary shape should be taken into account.
Figure 8.27:Species concentrations and the solution potential at the pit bottom as a function
of rcap/rpit calculated assuming a dissolution current density of 1 A/cm2
and different
boundary conditions: dotted lines: “no walls” ( 0, =Φ= ∞
ii cc ), solid lines: cylindrical
capillary with insulating walls, and dashed lines: real capillary shape with insulating walls.
Effect of homogeneous reactions (hydrolysis and aluminium chloride complexes)
As already discussed, the pit solution has lower pH values compared to the bulk solution.
Hydrolysis reactions are responsible for this difference and the most important of those is the
first reaction (5).
Now consider a model including 10 species: Na+
, Cl-
, H+
, OH-
, Al3+
, AlOH2+
, Al2(OH)2
4+
,
AlCl2+
, Al(OH)Cl+
, and Al(OH)2Cl and 7 homogeneous reactions (4-10). Kinetic constants
for all these reactions were found in the literature and the rate equations for the reactions were
derived explicitly (see lecture slides). All the calculations were performed assuming NaCl
solution with a bulk concentration of 1 M and a bulk pH of 6.The dependence of the pH on
the dissolution current density for the “no walls” boundary condition is shown in Fig. 8.28
together with the expression which allows one to perform estimation of the pH values at the
pit bottom for a given dissolution current density in a quick arithmetic calculation.
0.01
0.1
1
10
100
10 100 1000rcap/rpit
speciesconcentration[M]orpotential[V]
potential, no walls [Na ], no walls [Cl ], no walls [Al ], no walls
potential, insulating wall [Na ], insulating wall [Cl ], insulating wall [Al ], insulating wall
potential, real capillary [Na ], real capillary [Cl ], real capillary [Al ], real capillary+
+
+
_
_
_
3+
3+
3+

0.000001
0.0001
0.01
1
100
-800 -700 -600 -500 -400
E vs SCE (mV)
log[abs(I,[nA])]
Figure 8.28: The pH, the concentration of chloride, and the potential values at the pit bottom
as a function of the dissolution current density for the “no walls” boundary condition.
8.4.4 Modelling of pitting in matrix of Al 2024 alloy
Experimental input
As a next example consider 3D-modelling of pitting in matrix of Al 2024 alloy, which has the
following alloy composition: Al: 95%, Cu: 3.5%, Mg: 1.5%. Therefore, in the model Cu2+
and Mg2+
ions should be taken into account. Fig. 8.29a shows a micropolarisation
measurement in 1 M NaCl solution using a capillary with an end diameter of 30 µm. The
measurement was stopped as the current achieved about 50 nA. Approximately 20 randomly
distributed corrosion pits with diameters varying from 0.2 to 0.6 µm appeared on the sample
surface after the measurement (Fig. 8.29b).
a) b)
Figure 8.29: (a) A micropolarisation curve measured on a matrix of Al 2024 using a capillary
with an rcap = 15 µm and (b) the sample surface after the polarization experiment
0
2
4
6
0.000001 0.0001 0.01 1
j Al [A/cm
2
]
pHor[Cl
-
][M]
0
0.02
0.04
0.06
potential[V]
pH
Cl
potential
fitting pH
pH = -0.5351 log(j Al) + 2.8259

In the model, the following species are considered: Na+
, Cl-
, H+
, Al3+
, AlOH2+
, Cu2+
, Mg2+
with the only one homogeneous reaction: Al3+
+ H2O AlOH2+
+ H+
. All the calculations
were performed assuming NaCl solution with a bulk concentration of 1 M and a bulk pH of 6.
Geometry and boundary conditions
For the model, a 3D geometry has been chosen. A cylindrical capillary with a radius of 15 µm
and a capillary height of 1 mm is placed over the sample surface, where 20 identical
hemispherical pits with a radius of 0.2 µm each are randomly distributed (Fig. 8.30). Adaptive
mesh consisting of triangular Lagrange-quadratic elements with a more dense mesh inside the
pits and less dense outside is shown in Fig. 8.30b. It is assumed that the anodic dissolution
occurs only at the pit surfaces. The current density of the anodic dissolution, j, was estimated
as the total current divided by sum of the actively dissolving pit surfaces. For a maximal total
current of 50 nA measured in the micropolarisation experiment (Fig. 8.30) the calculated
current density is 0.2 A/cm2
.
(a) (b)
Figure 8.30 Model geometry (a), mesh (b)
The following boundary conditions were applied:
• At the top of the capillary: 0, =Φ= ∞
ii cc , where ci
∞
is the bulk concentration of
species i.
∞
+
H
c = 1 · 10-6
M, for all Al-, Cu- and Mg- containing species, ci
∞
are set to
zero (“no walls”).
• At the capillary wall, two types of boundary conditions are imposed: either “insulating
wall” or “no walls”.
• At the capillary bottom, excluding the pit surfaces, the insulating condition is
assumed.
• At the pit surface boundaries, three metal dissolution reactions occur: Al Al3+
+ 3e−
with a current density of jAl, Mg Mg2+
+ 2e−
with a current density of jMg, Cu
Cu2+
+ 2e−
with a current density of jCu, giving the values for the fluxes of Al3+
, Mg2+
,

and Cu2+
ions as
F
j
3
Al
,
F
j
2
Mg
, and
F
j
2
Cu
, respectively. Taking into account the
composition of the alloy, this leads to the following ratio of the partial current
densities for Al3+
, and Cu2+
, Mg2+
, 0.95 jAl,: 0.035 jCu,: 0.015 jMg
( MgCuAl 015.0035.095.0 jjjj ++= )
Results
Figures 8.31 and Figures 8.32 show the results of calculations performed for a dissolution
current density of 0.2 A/cm2
assuming “no walls” boundary condition. Because of their
random location some pits are located close to each other, whereas others are “standing
alone”. Therefore, for the analysis, two pits were chosen: pit 1, located in the vicinity of the
capillary edge with far away neighbouring pits, and pit 2, located approximately in the middle
of the capillary with neighbouring pits in the close proximity (see Fig. 9).
(a) (b)
Figure 8.31: pH value distribution over capillary bottom (a) and cross section (b) assuming
“no walls” boundary condition. Dissolution current density on pit surface is 0.2 A/cm2
.
3.5
4
4.5
5
5.5
0 1 2 3 4 5
z [µm]
pH
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
potential[V]
pH, pit 1
pH, pit 2
potential, pit 1
potential, pit 2
0.000001
0.00001
0.0001
0.001
0.01
0 1 2 3 4 5
z [µm]
speciesconcentration[M]
Al, pit 1 AlOH, pit 1
Cu, pit 1 Mg, pit 1
Al, pit 2 AlOH, pit 2
Cu, pit 2 Mg, pit 2
Figure 8.32: Centreline concentration and potential profiles upwards from the pit bottom,
calculated for two different pits: pit 1 (solid lines) and pit 2 (dashed lines) assuming “no
walls” boundary condition. The dissolution current density on pit surfaces is 0.2 A/cm2
.
pit 1 pit 2 pit 1 pit 2

For the “no walls” boundary condition (Fig. 8.31) and a dissolution current density of 0.2
A/cm2
, the difference in concentrations between pit 1 and pit 2 for all species and the solution
potential with the exception of Na+
and Cl-
, at the pit bottom is about 10-15 %; that changes
considerably with the elevation. For example, at a height of 1 µm above the pit bottom, the
difference reaches already 50-70 % (Fig. 8.32).
8.4.5 Modelling of intergranular corrosion in Al 2024 alloy
Finally, the model can be extended to the case of intergranular corrosion. Figure 8.33 shows a
typical intergranular attack for 2024-T3 alloy with the corresponding experimental local
current density measured by means of the microcapillary technique. The electrochemical
input data in this case is the dissolution current of: j ≈ 0.01 A/cm2
Figure 8.33: Al alloy 2024 with sample surface (top SEM image) and cross section after
severe intergranular attack (bottom SEM image) and (right) typical microcapillary local
electrochemical anodic polarization curves for 2024-T3 0.5M NaCl (pH 7)
The geometry of the model has been chosen to simulate a deep crevice formed during
intergranular attack, Fig. 8.34. The typical dimensions used are a capillary radius of 25 µm,
and an height of 5 mm. The crevice radius is defined as 0.05 µm with a depth 1mm or
0.1 mm. The anodic dissolution is at the crevice bottom and two different locations are
defined for the intermetallics serving as cathodes:
- Surrounding cathode “out”: at 10 µm from axis, width 0.1 µm
- Cylindrical cathode “in”: 50 µm up from bottom, width 2.5 µm

Figure 8.34: Schematic description of the geometry, species considered and location of the
cathodes
The following assumptions are made for the model:
• Capillary top: “no walls” and bulk concentrations for all species
• Anode: metal dissolution
• Cathode: oxygen reduction
• Current at cathodic boundary:
where sanode and scathode are anodic and cathodic areas
Based on this model, the pH, concentrations of O2 and Cl-
at crevice bottom can be derived as
a function of the active dissolution current density. It is important to remember that in a
corrosion process, anodic and cathodic reaction rates have to be equal at any time. The
position of the cathodes therefore plays a crucial role and will change the crevice media
properties. One consequence is that calculations for cases. (i) cathode “in” and (ii) cathodes
“in” and “out” cannot be done for higher dissolution current densities because of complete
0, =Φ= ∞
ii cc
F
jAl
3
nN 3
Al
=⋅+Al → Al
3+
+ 3 e
-
O2
+ 2H2
O + 4e
-
4OH
-
)( 21
2
cathodecathode
anodeAl
O
ss
sj
j
+
=
F
j
4
2
2
O
O −=⋅nN F
j 2
-
O
OH
=⋅nN

oxygen depletion in the crevice, Fig. 8.35c. Another major difference of having a cathode in
the crevice formed by the intergranular attack is that due to oxygen reduction, the pH will not
get acidic (Fig. 8.35a) and the autocatalytic process for localized corrosion mechanisms
described earlier will not take place. Concerning the chloride concentration, no differences
will be found from small to intermediate corrosion current densities, Fig. 8.35b.
a) b)
2
4
6
8
10
1E-07 1E-06 0.00001 0.0001 0.001 0.01 0.1
jAl [A/cm
2
]
pH
cathode "out"
cathode "in"
cathode "in" and "out"
0
1
2
3
4
1E-07 0.000001 0.00001 0.0001 0.001 0.01 0.1
jAl [A/cm
2
]
concentrationCl
-
[M]
cathode "out"
cathode "in"
c)
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
1E-07 1E-06 0.00001 0.0001 0.001 0.01 0.1
jAl [A/cm
2
]
concentrationO2[M]
cathode "out"
cathode "in"
Figure 8.35: Evolution of three major parameters as function of the location of the cathodes:
(a) pH, (b) chloride concentration, (c) oxygen concentration
A final comparison can be performed, related to the pH values evolution at the crevice bottom
as a function of dissolution current density, and this for different models of active cathode in
intergranular attacks (crevice depths) of 1 mm and 0.1 mm in depth, Fig. 8.36. The pH
evolution trends are similar, only the variations are more pronounced for deep attacks what is
in accordance with the tomography results for example. In relation with these previous
results, it was mentioned that the aggressivity of the solution is increasing in deep attacks
because the solution exchange is getting more and more difficult in deep crevices.

a) b)
2
3
4
5
6
7
8
0.0000001 0.00001 0.001 0.1
jAl [A/cm
2
]
pH
0.1 mm
1 mm
7
7.5
8
8.5
9
9.5
10
0.0000001 0.000001 0.00001 0.0001
jAl [A/cm2
]
pH
0.1 mm
1 mm
c)
2
3
4
5
6
7
8
1E-07 0.000001 0.00001 0.0001 0.001
jAl [A/cm2
]
pH
0.1 mm
1 mm
Figure 8.36: pH evolution in intergranular attacks of two different depth (1mm and 0.1mm)
as function of the locations of the cathodes: (a) cathode out, (b) cathode in, (c) cathode in +
cathode out
Summary
- 2D and 3D mathematical models for simulating localized corrosion processes in the
case of a passive Al-alloy surface with pits in which active electrochemical metal
dissolution occurs has been developed. The models include hydrolysis products of
aluminium and species obtained as a result of homogeneous reactions between
chloride and Al3+
ions and Al hydrolysis products.
- Predictions for the potential values and the species concentrations are conducted
assuming different dissolution current densities. It is confirmed that current densities
exceeding 0.1 A/cm2
can be identified as “active dissolution”, because they
significantly affect the values of the potential and the species concentrations. The
acidity in the pit can be explained by the hydrolysis of Al3+
.
- As a clear benefit, the modelling approach developed allows to realistically study the
influence of microelectrochemical experimental setups on the modelling parameters
of single localized corrosion events. And in turn, the modelling results can serve as a
feedback for improving the electrochemical experimental setups.

- First mathematical model for simulating intergranular corrosion has been developed.
The model includes metallic ionic species resulting from electrochemical reactions
at the metal-solution interface (heterogeneous reactions) and reactions in solution
(homogeneous reactions).
- Model includes one anodic site at crevice bottom and cathodic sites on sample
surface (cathode “out”) and in crevice (cathode “in”).
- It is shown that corrosion propagation requires electrical coupling between the
anodic site in the crevice and the cathodic sites on the sample surface (cathode
“out”), resulting in high dissolution rates. If only cathode “in” is active, the attack
will propagate with slower rates depending on crevice depth due to oxygen depletion
in the crevice (ex. for 1-mm crevice 10-5
A/cm2
(0.11 mm/year)).
- Active cathode “out”, or both, cathodes “in” and “out”, lead to acidic conditions, and
active cathode “in” to alkaline conditions in the crevice

ch8_intergranular_corrosion

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